iCloud Backup

If you have an iCloud backup and you have iCloud Photos "On", then yes, your pictures will be there in your new phone after you restore from iCloud.

To check, tap "Settings" on your phone, then (Your Name) at the top then iCloud, then make sure iCloud Photos is on.

Your welcome! I understand, because I would be devastated if I lost my photos. I a.lso keep a local backup of my photos on my computer

One more thing, you can check the status of your last iCloud backup by tapping this on your iPhone:

It will tell you when you last backup was made, and you can also tap "BackUp Now" if you want.

Also, you can read more here: https://www.apple.com/icloud/

Yes, as long as you have Contacts "on" on the iCloud page in settings. See below: